Question

Find S10 for the series 2 + 7 + 12 + 17 +...

Answer 1

\[\begin{align*}S_{10}&=\sum_{n=1}^{10}(2+5(n-1))\\
&=2\sum_{n=1}^{10}1+5\left(\sum_{n=1}^{10}n-\sum_{n=1}^{10}1\right)
\end{align*}\]
Now use the following formulas:
\[\sum_{n=1}^{k}1=k\\
\sum_{n=1}^{k}n=\frac{k(k+1)}{2}\]
(In this case, \(k=10\).)

Answer 2

sum = n/2(2a + (n - 1)d
n = 10
d = 5
a = 2
lets sub it in...
s10 = 10/2 * (2*2 + (10 - 1)* 5
s10 = 5 * (4 + 9) * 5
s10 = 5 (13 * 5)
s10 = 5(26)
s10 = 130